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What are some recommended books, online sources, and applications (PC or Android platform) for becoming good at math?

I am specifically looking for books, online resources, and apps that will refresh my knowledge from the beginning of basic math to learning the curriculum of most undergrad math majors.

I initially googled "how do I become good at math?" and I read an article "Five Ways to be Better At Math" which mentioned mathoverflow.net:

"If all else fails, go to some math forums (like Math Overflow) and ask for book recommendations, telling them you want to become good at math and not just pass a required course; give them specific details and they can help find a book perfect for you."

http://www.xamuel.com/five-ways-to-be-better-at-math/

Upon asking my particular question on mathoverflow, I received this answer: "MathOverflow is for questions relevant to research mathematics. You should ask this question on math.stackexchange.com instead. – Qiaochu Yuan 2 mins ago"

This question is found here: http://mathoverflow.net/questions/86505/what-are-some-recommended-books-online-sources-and-applications-pc-or-android

Google and Android market has also found some online sources and apps relevant to my query:

"A+ Click Math Skill Test for K-1 K-12"

www.aplusclick.com

"Math Workout - the most popular brain training app on Android"

www.mathsworkout.net

My background is not in mathematics, but it is in the social sciences, specifically, archaeology. My pre-college math curriculum consisted of arithmetic, geometry, algebra, and pre-calculus. In my undergrad I took a course in business math, logic, and statistics. Assessment of understanding in these courses was equivalent to a grade C. I received a bachelors in anthropology in 2009.

I am now in the workforce, gathering experience in my field and deciding where to go from here. As of now, I would like to design my own projects and go into academia. My theoretical orientation is simply geoarchaeology or "using geology to do archaeology." This covers not only geology and archaeology, but anthropology as well, and chemistry, physics, ecology, and mathematics. Grandly speaking, mathematics provides a chain of theoretical models for the natural world, and so I would like to start from there. I have the time and isolation to learn (I'm a field archaeologist who lives in the back country).

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closed as not constructive by lhf, Asaf Karagila, Pete L. Clark, Henning Makholm, Quixotic Feb 8 '12 at 7:45

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3 Answers 3

up vote 1 down vote accepted

I'll answer the following "less specific" question, What are some good practices to strengthen one's mathematical skills?

At this point, I should note the following: broadly speaking, one has "mathematical skills" (for lack of a better term) which includes logical deduction, proofwriting, proofreading, and so forth, and one has "computational skills" which includes things like being able to add, multiply, divide, factor, etc. things quickly.

The former is more complicated, and it is what courses "above" calculus in colleges generally teach students of mathematicians; it includes learning subjects like Real and Complex Analysis, Point-Set and Algebraic Topology, and Abstract Algebra, among others. If you would like to get a background in these things then perhaps search for what colleges require for undergraduate math majors and take a look at the books and homework they use in those courses. If, though, you only would like to learn things like (high school) algebra, geometry, calculus, or statistics, ordinarily there are a number of very cheap old editions of books on sites like Amazon. If you have a lot of time to sit around, it may be helpful to take a few books and attempt to work through the exercises.

To become better at computational mathematics, one must simply practice. Speed Arithmetic books (you can usually find these fairly cheaply or in a library) will have hundreds of exercises to make the reader better at adding and multiplying quickly and efficiently. One of my teachers in high school told us that whenever we saw a number, we should prime factorize that number in our heads (this is something I still do, and recommend!).

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Take a look at http://www.khanacademy.org/ on mathematics. If you are serious about this, your best bet is spending some money with genuine online courses that have some feedback features. Online colleges in the U.S. are fairly young. I understand there are such courses in England that are well regarded, including some that give Ph.D.'s. Bear in mind how very important is homework in this scheme, that is when you learn the material. As when I learned to ski, one ought to alternate hearing how it ought to be done from the coach with practice on one's own.

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you should also have a look at "Maths Bug" on the android. Covers basic maths skills up to Fractions, percentages, algebra and shapes. Includes multiple game modes and built in hints & tips.

See http://maths.ecowho.com/ for more details.

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